Sensitivity analysis in linear semi-infinite programming: Perturbing cost and right-hand-side coefficients

This paper analyzes the effect on the optimal value of a given linear semi-infinite programming problem of the kind of perturbations which more frequently arise in practical applications: those which affect the objective function and the right-hand-side coefficients of the constraints. In particular, we give formulae which express the exact value of a perturbed problem as a linear function of the perturbation.     

Existence and uniqueness of v-asymptotic expansions and Colombeau's generalized numbers

We define a type of generalized asymptotic series called v-asymptotic. We show that every function with moderate growth at infinity has a v-asymptotic expansion. We also describe the set of v-asymptotic series, where a given function with moderate growth has a unique v-asymptotic expansion. As an application to random matrix theory we calculate the coefficients and establish the uniqueness of the v-asymptotic expansion of an integral with a large parameter. As another application (with significance in the non-linear theory of generalized functions) we show that every Colombeau's generalized number has a v-asymptotic expansion. A similar result follows for Colombeau's generalized functions, in particular, for all Schwartz distributions.     

Enriques Surfaces, Analytic Discriminants, and Borcherds's Φ Function

In [Bor 96], Borcherds constructed a non-vanishing weight 4 modular form Φ on the moduli space of marked, polarized Enriques surface of degree 2 by considering the twisted denominator function of the fake monster Lie algebra associated to an automorphism of order 2 of the Leech lattice fixing an 8-dimensional subspace. In [JT 94] and [JT 96], we defined and studied a meromorphic (multi-valued) modular form of weight 2, which we call the K3 analytic discriminant, on the moduli space of marked, polarized, K3 surfaces of degree 2d; in certain cases, including when , where p _k are distinct primes, our meromorphic form is actually a holomorphic form. Our construction involves a determinant of the Laplacian on a polarized K3 surface with respect to the Calabi-Yau metric together with the L ² norm of the image of the period map with respect to a properly scaled holomorphic two form. Since the universal cover of any Enriques surface is a K3 surface, we can restrict the K3 analytic discriminant to the moduli space of degree 2 Enriques surfaces. The main result of this paper is the observation that the square of our degree 2 analytic discriminant, viewed as a function on the moduli space of degree 2 Enriques surfaces, is equal to the Borcherd's Φ function, up to a universal multiplicative constant. This result generalizes known results in the study of generalized Kac-Moody algebras and elliptic curves, and suggests further connections with higher dimensional Calabi-Yau varieties, specifically those which can be realized as complete intersections in some, possibly weighted, projective space. Received: 24 July 1995 / Accepted: 21 March 1997     

Nuclear reactions induced by stopped negative pions in133Cs,93Nb and45Sc

The energy and angular distributions ofp, d, t,³He and⁴He from the three targets Cu, Ag and Au were measured at five different angles for bremsstrahlung with peak energy 500MeV. The measurements were made using a telescope consisting of four surface-barrier detectors. The experimental data are compared with cascade-evaporation calculations. For the⁴He-distributions the calculations were extended to include the contribution from knock-out of surface alphas by the cascade nucleons. The comparison shows that the main contribution comes from evaporation but that there is a direct component of the order of 10%.     

On the covariant structure of the two-point function

The spectral representation of the two-point function for arbitrary fields proposed recently [1] is rigorously proved and analyzed. The problem is treated in momentum space where the covariant structure is simpler because of the spectrum conditions. For finite-component fields the explicit matrix structure is found in coordinate space too and is applied to the definition of time-ordered Green functions for arbitrary spin. The decomposition of the two-point function into kernels of definite spin is carried out in the general case, a necessary and sufficient condition for the growth of the coefficients in this decomposition being given. The positive-definiteness condition (in the case of Hermitian conjugate fields) is fulfilled automatically by the elementary kernels.The formalism of homogeneous distributions in two dimensional complex domain [2] is used throughout the paper.On leave of absence from Joint Institute for Nuclear Research, Dubna, USSR and from Physical Institute of the Bulgarian Academy of Sciences, Sofia, Bulgaria.     

A simple automatic system using the HP-85 microcomputer for programmed potentiometric titration

A simple way of constructing an automatic titration system is proposed, based on combination of a digital pH-meter and an automatic burette with an HP-85 microcomputer. An inexpensive interface unit based on a MOTOROLA 6800 has been developed, which permits communication of the computer with the pH-meter and the burette. The system constructed is very flexible and can find wide application in potentiometric titration and direct potentiometry with different kinds of ion-selective electrodes.     

Scale and conformal covariance in quantum electrodynamics

The paper consists of two independent parts. First, we review the situationin scale invariant massless QED from an axiomatic standpoint. Assuming that the τ-functions (or, equivalently, the Euclidean Schwinger functions) transform covariantly under dilatations, we deduce that the current j_τ(x) has zero n-point Wightman functions, but nonvanishing τ-functions. Assuming in addition conformal invariance of the current-field vertex function, we write down a bootstrap equation similar to the one derived in [7] from the point of view of pertubation theory. Next we consider a non-Lagrangian, conformal invariant model of interacting antisymmetric tensor field F_μv (of scale dimension d) and Dirac field ψ (of dimension d'. The model involves two conserved currents (an “electric” and a “magnetic” one) and two effective coupling constants. We demonstrate that it is free of ultravioletdivergences in the range of dimensions $\text{2 < d < 3,}\text{3}\text{2}\text{< d′ <}\text{5}\text{2}$.     

Limite de convexité d'une classe de Nevanlinna de fonctions analytiques

Sans résumé     

On the possible multi-valuedness of quantum wavefunctions

A theorem generalizing a result due to Schrödinger on the possible multi-valuedness of quantum wavefunctions is proved. Relevant examples show that double-valued wavefunctions do exist, at least in problems of a theoretical interest.